3,157 research outputs found
Justification of c-Number Substitutions in Bosonic Hamiltonians
The validity of substituting a c-number for the mode operator
is established rigorously in full generality, thereby verifying one aspect of
Bogoliubov's 1947 theory. This substitution not only yields the correct value
of thermodynamic quantities like the pressure or ground state energy, but also
the value of that maximizes the partition function equals the true
amount of condensation in the presence of a gauge-symmetry breaking term -- a
point that had previously been elusive.Comment: RevTeX4, 4pages; minor modifications in the text; final version, to
appear in Phys. Rev. Let
A nonlinear indentity for the scattering phase of integrable models
A nonlinear identity for the scattering phase of quantum integrable models is
proved.Comment: 5 pages, Latex, no figure
Ground State Energy of the Low Density Bose Gas
Now that the properties of low temperature Bose gases at low density, ,
can be examined experimentally it is appropriate to revisit some of the
formulas deduced by many authors 4-5 decades ago. One of these is that the
leading term in the energy/particle is , where is
the scattering length. Owing to the delicate and peculiar nature of bosonic
correlations, four decades of research have failed to establish this plausible
formula rigorously. The only known lower bound for the energy was found by
Dyson in 1957, but it was 14 times too small. The correct bound is proved here.Comment: 4 pages, Revtex, reference 12 change
Improved Lieb-Oxford exchange-correlation inequality with gradient correction
We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb
energy of a general many-particle quantum state, with a lower constant than the
original statement but involving an additional gradient correction. The result
is similar to a recent inequality of Benguria, Bley and Loss, except that the
correction term is purely local, which is more usual in density functional
theory. In an appendix, we discuss the connection between the indirect energy
and the classical Jellium energy for constant densities. We show that they
differ by an explicit shift due to the long range of the Coulomb potential.Comment: Final version to appear in Physical Review A. Compared to the very
first version, this one contains an appendix discussing the link with the
Jellium proble
On the flux phase conjecture at half-filling: an improved proof
We present a simplification of Lieb's proof of the flux phase conjecture for
interacting fermion systems -- such as the Hubbard model --, at half filling on
a general class of graphs. The main ingredient is a procedure which transforms
a class of fermionic Hamiltonians into reflection positive form. The method can
also be applied to other problems, which we briefly illustrate with two
examples concerning the model and an extended Falicov-Kimball model.Comment: 23 pages, Latex, uses epsf.sty to include 3 eps figures, to appear in
J. Stat. Phys., Dec. 199
Effect of electronic interactions on the persistent current in one-dimensional disordered rings
The persistent current is here studied in one-dimensional disordered rings
that contain interacting electrons. We used the density matrix renormalization
group algorithms in order to compute the stiffness, a measure that gives the
magnitude of the persistent currents as a function of the boundary conditions
for different sets of both interaction and disorder characteristics. In
contrast to its non-interacting value, an increase in the stiffness parameter
was observed for systems at and off half-filling for weak interactions and
non-zero disorders. Within the strong interaction limit, the decrease in
stiffness depends on the filling and an analytical approach is developed to
recover the observed behaviors. This is required in order to understand its
mechanisms. Finally, the study of the localization length confirms the
enhancement of the persistent current for moderate interactions when disorders
are present at half-filling. Our results reveal two different regimes, one for
weak and one for strong interactions at and off half-filling.Comment: 16 pages, 21 figures; minor changes (blanks missing, sentences
starting with a mathematical symbol
Localization of Multi-Dimensional Wigner Distributions
A well known result of P. Flandrin states that a Gaussian uniquely maximizes
the integral of the Wigner distribution over every centered disc in the phase
plane. While there is no difficulty in generalizing this result to
higher-dimensional poly-discs, the generalization to balls is less obvious. In
this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic
Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional
We extend the analysis of the Bogoliubov free energy functional to two
dimensions at very low temperatures. For sufficiently weak interactions, we
prove two term asymptotics for the ground state energy.Comment: revised versio
Charged and spin-excitation gaps in half-filled strongly correlated electron systems: A rigorous result
By exploiting the particle-hole symmetries of the Hubbard model, the periodic
Anderson model and the Kondo lattice model at half-filling and applying a
generalized version of Lieb's spin-reflection positivity method, we show that
the charged gaps of these models are always larger than their spin excitation
gaps. This theorem confirms the previous results derived by either the
variational approach or the density renormalization group approach.Comment: 20 pages, no figur
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